Plastic dislocation and incompatibility density as indicators for residual stresses

Residual stresses in forming simulations are typically investigated by analyzing the remaining stress state after removing all external loadings. However, the generation of the stress state during forming remains unknown. As a remedy, we use the plastic and elastic dislocation and incompatibility densities - derived from continuum mechanical and differential geometrical considerations - as indicators to track the generation of residual stresses through out a forming operation. Theoretical backgrounds for small and large strain plasticity are highlighted and practical aspects regarding implementation are provided. Two examples demonstrate the functionality of the approach, whereby the plastic incompatibility density in phenomenological, multiplicative large strain plasticity serves as indicator

Inverse form finding with h-adaptivity and an application to a notch stamping process

The aim is to determine the optimized semi-finished workpiece geometry to its given target geometry after a forming process. Hereby, a novel approach for inverse form finding, a type of a shape optimization, is applied to a notch stamping process. As a special feature, h-adaptive mesh refinement is considered within the iteratively performed forming simulation

Case Study on the Influence of Kinematic Hardening within a Parameter-free and Non-invasive Form Finding Approach

Inverse form finding – as a type of shape optimization – aims in determining the optimal preform design of a workpiece for a specific forming process, whereby the desired target geometry is known. Recently, a novel parameter-free and heuristic approach was developed to tackle this nonlinear optimization problem. Benchmark tests already delivered promising results. As a particular note-worthy feature of the approach, a coupling to an arbitrary finite element software is feasible in a non-invasive fashion. The aim of this contribution is to investigate the effect of kinematic hardening and cyclic loading on the convergence behavior of the algorithm

On a recursive formulation for solving inverse form finding problems in isotropic elastoplasticity

Background: Inverse form finding methods allow conceiving the design of functional components in less time and at lower costs than with direct experiments. The deformed configuration of the functional component, the applied forces and boundary conditions are given and the undeformed configuration of this component is sought. Methods: In this paper we present a new recursive formulation for solving inverse form finding problems for isotropic elastoplastic materials, based on an inverse mechanical formulation written in the logarithmic strain space. First, the inverse mechanical formulation is applied to the target deformed configuration of the workpiece with the set of internal variables set to zero. Subsequently a direct mechanical formulation is performed on the resulting undeformed configuration, which will capture the path-dependency in elastoplasticity. The so obtained deformed configuration is furthermore compared with the target deformed configuration of the component. If the difference is negligible, the wanted undeformed configuration of the functional component is obtained. Otherwise the computation of the inverse mechanical formulation is started again with the target deformed configuration and the current state of internal variables obtained at the end of the computed direct formulation. This process is continued until convergence is reached. Results: In our three numerical examples in isotropic elastoplasticity, the convergence was reached after five, six and nine iterations, respectively, when the set of internal variables is initialised to zero at the beginning of the computation. It was also found that when the initial set of internal variables is initialised to zero at the beginning of the computation the convergence was reached after less iterations and less computational time than with other values. Different starting values for the set of internal variables have no influence on the obtained undeformed configuration, if convergence can be achieved. Conclusions: With the presented recursive formulation we are able to find an appropriate undeformed configuration for isotropic elastoplastic materials, when only the deformed configuration, the applied forces and boundary conditions are given. An initial homogeneous set of internal variables equal to zero should be considered for such problems

A non-invasive node-based form finding approach with discretization-independent target configuration

Form finding is used to optimize the shape of a semi-finished product, i.e. the material configuration in a forming process. The geometry of the semi-finished product is adapted so that the computed spatial configuration corresponds to a prescribed target spatial configuration. Differences between these two configurations are iteratively minimized. The algorithm works non-invasively, thus there is a strict separation between the form update and the finite element (FE) forming simulation. This separation allows the use of arbitrary commercial FE-solvers. In particular, there is no need for a modification of the FE forming simulation, only the material configuration is iteratively updated. A new method is introduced to calculate the difference between the target and the computed spatial configuration. Thereby the target mesh is separated from the mesh for the FE forming simulation, which enables a more accurate and independent representation of the target configuration. In addition, the possibility of taking into account manufacturing constraints in the optimization process is presented. The procedure is illustrated for the example of the first stage of a novel two-stage sheet-bulk metal forming process

Studien zur Villacher Heinrich-Werkstätte

Die jüngere Villacher Hauptwerkstätte oder Heinrich-Werkstätte ist eine von mehreren stilistisch zu unterscheidenden Bildschnitzerwerkstätten des ersten Viertels des 16. Jahrhunderts in Kärnten. Sie zeichnet sich durch eine sehr hohe Produktivität und einen breiten Einflussbereich aus. Der Werkkomplex repräsentiert eine klassizierende Stilistik, für die insbesondere eine spezifische beruhigte Variante des Parallelfaltenstils und eine gänzlich „materialunspezifische“ Oberflächenbehandlung charakteristisch sind. Eine Anzahl unterschiedlicher Tafelmaler war an den Flügelaltären der Heinrich-Werkstätte tätig. Die zentrale Thematik dieser Arbeit ist die Untersuchung dieser Malereien, wobei einerseits Zuschreibungsfragen bearbeitet, andererseits insbesondere die möglichen Zusammenhänge und gegenseitigen Einflüsse zwischen den einzelnen Malern betrachtet werden. Es ergibt sich insgesamt das Bild einer vorrangig an Nürnberger und Augsburger Vorbildern orientierten Villacher „Renaissance“-Malerei, die sich etwa ab 1514/15 in engem Zusammenhang mit der Heinrich-Werkstätte entwickelte, in ihrem Wirkungsradius aber auch auf die verschiedenen Zweigwerkstätten bis nach Osttirol ausgriff. Im Zuge der Einzelbetrachtungen wird auch der – von der Forschung mehr beachtete - schnitzplastische Anteil der jeweiligen Flügelaltäre der Heinrich-Werkstätte in den Blick genommen und hinsichtlich seiner Positionierung innerhalb des Gesamtwerkes überprüft. Der Zusammenhang des urkundlich genannten Bildschnitzers Heinrich von Villach mit der Werkgruppe wird in Hinblick auf seine Plausibilität diskutiert

The scope and consequences of metaphoric thinking: Using individual differences in metaphor usage to understand how metaphor functions.

People often think, feel, and behave metaphorically according to conceptual metaphor theory. There are normative sources of support for this theory, but individual differences have received scant attention. This is surprising because people are likely to differ in the frequency with which they use metaphors and therefore the frequency with which they experience the costs and benefits of metaphoric thinking. To investigate these ideas, a five study program of research (total N = 532) was conducted. Study 1 developed and validated a metaphor usage measure, finding that people were fairly consistent in their tendencies toward literal thought and language on the one hand versus metaphoric thought and language on the other. These differences were, in turn, consequential. Although metaphor usage predicted susceptibility to metaphor transfer effects (Studies 2-3), it was also linked to higher levels of emotional understanding (Studies 4-5). The findings provide support for several key premises of conceptual metaphor theory in the context of a new measure that can be used to track the consequences of metaphoric thinking

A novel continuum approach to gradient plasticity based on the complementing concepts of dislocation and disequilibrium densities

A geometrically linear continuum mechanics framework is proposed for gradient plasticity combining ’strain gradients’ and, with a novel approach, ’stress gradients’. Thereby the duality of kinematic and kinetic quantities is exploited in view of the ’div-grad-curl orthogonality’ in continuum field theories. On the one hand the non-integrability of the plastic distortion results in the well-established dislocation density - often denoted as the geometrically-necessary-dislocation (GND) density - that enters the energy storage function. On the other hand - as entirely novel concept introduced in this contribution - the non-equilibrium of the plastic stress results in the disequilibrium density that parameterizes the dual dissipation potential within the convex analysis setting of plasticity. Consequently both, the dislocation density as well as the disequilibrium density contribute in modelling the size-dependent hardening state of a material in a continuum mechanics setting. The novel approach is eventually elucidated in much detail for the specific case of single crystal plasticity